The Journal of Bone & Joint Surgery

The Journal of Bone & Joint Surgery, Volume 88, Issue suppl 2

Workshop Articles | April 01, 2006

Modeling Changes in Intervertebral Disc Mechanics with Degeneration

Raghu N. Natarajan, PhD; Jamie R. Williams, PhD; Gunnar B.J. Andersson, MD, PhD

In support of their research for or preparation of this manuscript, one or more of the authors received grants or outside funding from the National Institutes of Health (NIH:AR 48152-02). None of the authors received payments or other benefits or a commitment or agreement to provide such benefits from a commercial entity. No commercial entity paid or directed, or agreed to pay or direct, any benefits to any research fund, foundation, educational institution, or other charitable or nonprofit organization with which the authors are affiliated or associated.

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J Bone Joint Surg Am, 2006 Apr 01;88(suppl 2):36-40. doi: 10.2106/JBJS.F.00002

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Abstract

Mechanical response of the spine to various dynamic loading conditions can be analyzed by way of in vitro and in vivo studies. Ethical concerns, interpretation of conclusions reached in animal studies, and lack of detailed stress distributions in the disc components are the major disadvantages of relying solely on in vivo studies. Intraspecimen variability, difficulty in including muscle activity, and inability to mimic fluid exchange into the disc during unloading are some of the disadvantages of in vitro models. The poroelastic finite element models can provide a method of understanding the relationship between biomechanical performance of the disc due to cyclic loading and disc degeneration. A poroelastic finite element model, including regional variation of strain-dependent permeability and osmotic pressure, was used to study the effect of disc degeneration on biomechanical properties as well as propagation of failure in the disc components when cyclic loading was applied to the lumbar disc. The results predicted that healthy discs were much more flexible than degenerated discs, and the disc stiffness decreased with increasing the number of load cycles independent of degenerative condition. Failure was found to progress as the drained elastic properties of the disc components decreased due to the presence of failure.

Poroelastic finite element modeling, including strain-dependent permeability and osmotic pressure, is the most advanced analytical tool currently available that can be used to understand how cyclic loading affects the biomechanical characteristics of a degenerated lumbar disc. However, a complete understanding of behavior of the intervertebral disc will ultimately be achieved only with use of a combination of computational models together with in vitro and in vivo experimental methods.

Finite element models of discs with varying degrees of disc degeneration will help clinicians understand the initiation and progression of disc failure and degeneration and will assist in the development of approaches to stimulate the regeneration of disc tissues.

Figures in this Article

The degenerative process of the lumbar disc is a cascading event that is often attributed to the cumulative damage caused by heavy physical work, lifting, stationary work postures, and vibrations. Consequently, it is important to understand how spinal motion segments react to cyclic loading conditions that are related to various physical activities.

Due to the invasiveness of the procedures and concerns involving the care and use of animals, a limited number of in vivo studies have been conducted with use of animal models such as bovine, murine¹, feline, and porcine models. These animal models have provided only limited information regarding how dynamic stiffness increases with cyclic loading, load magnitude, and frequency of loading². In vivo experiments do not provide insight into the distribution of stresses in various components of the disc, which is essential to understanding the initiation and progression of any structural damage to the disc. Although a large amount of experimental results based on cadaver testing are available in the literature, measurements alone are not sufficient to clarify the nature of correlation between mechanical loads and disc degeneration. This is because of the technical complexities that preclude measurements of the state of stress and displacements throughout the motion segment as well as the difficulty of experimental simulation of the pathology of the unit as it exists in various stages of disc degeneration.

Accordingly, the need for the development of a numerical model of the disc, such as a finite element model, to supplement experimental studies has been recognized³. A strength of the finite element model is the ability to parametrically alter one input factor and evaluate the effect on the results.

The objective of this article is to review the most recent advances in the development of finite element models that address the issue of lumbar disc degeneration. Finite element models have been refined by including poroelastic material properties of various components of the motion segment and by including certain physiologic parameters (such as strain-dependent permeability, porosity, and regional variation of poroelastic material properties within the motion segment model) to better predict the relationship between disc degeneration and cyclic loading.

Poroelastic Finite Element Models of Disc Degeneration

Poroelastic Finite Element Models of Disc Degeneration | Effect of Degeneration on Disc Biomechanical Properties | Poroelastic Finite Element Model to Predict Initiation and Progression of Disc Failure | Conclusions and Discussion | References

To understand the disc degeneration process, finite element models should include not only changes in geometry of the disc and altered mechanical properties of the nucleus but also changes in permeability and porosity of various disc components and the reduction in water content of the nucleus. Experimental observations have suggested that it is the decrease in fluid content in the disc that occurs due to degeneration, along with the nuclear material becoming more like the anular matrix, that makes the disc stiffer. In addition, the fluid phase may have an important effect on the mechanical response of the disc, which may affect the nutritional paths to the avascular interior of the disc. To this effect, a number of poroelastic finite element models have been developed^1,3-11.

Investigators^6,9 have developed a poroelastic finite element model that includes strain-dependent permeability and osmotic potential to investigate the disc mechanics associated with multiple cycles of creep compression and expansion. A one-dimensional model that included permeability and osmotic potential as functions of strain has been shown to be sufficient for modeling the time-dependent deformation of a lumbar motion segment in a multiple creep-compression-expansion loading experiment⁶.

Lotz et al.¹ combined an in vivo mouse model and a related poroelastic model (without the strain-dependent permeability and osmotic pressure) to study how compression can induce disc degeneration. Using an axisymmetric disc-body-disc proelastic finite element model, they showed that sustained compression load maintained tensile stresses in the outer portion of the anulus but that these stresses were lost in the middle and inner regions. These model predictions correlated well with the in vivo findings that the inner and middle portions of the anulus became progressively more disorganized with an increase in apoptosis and an associated loss of cellularity. Iatridis et al.⁷ developed a finite element model of a slice of lumbar disc material that included electric potential and chloride and sodium concentrations in addition to fluid flow in the disc. The results showed that changes in the fixed-charge density alone, from a healthy to a degenerate distribution, would cause an increase in solid matrix stresses and could cause fluid loss that may have implications for disc nutrition and modulation in cellular activities. Poroelastic finite element models have also been used to model nutrient transport changes with degeneration^12,13.

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Fig. 1: Effect of disc degeneration on biomechanical properties of discs subjected to cyclic loading. Normal discs were much more flexible than degenerated discs. Stiffness of the disc decreased as the load cycle increased. FEM = finite element model.

Natarajan et al.⁸ built a poroelastic finite element model and employed a unique approach to represent the interaction of fluid with the proteoglycans contained within the nucleus. This approach included an interaction term to represent how changes in fluid volume within the disc affected the biomechanics of the disc under various loading conditions. This model was then used to predict changes in the biomechanical behavior of lumbar discs due to disc degeneration and to simulate progression of disc changes subsequent to anular failure, to assist in understanding disc degeneration.

Effect of Degeneration on Disc Biomechanical Properties

With use of the custom poroelastic finite element code developed in our laboratory⁸, two different poroelastic finite element models of the intervertebral disc were created. One model was created to represent the normal healthy disc, and the other model represented a degenerated disc. The degenerated disc model was created by modifying the material properties of the inner and outer portions of the anulus and the nucleus, making use of values taken from the literature. Tables I, II, and III list the elastic and poroelastic material properties used for each of the finite element models for the outer portion of the anulus, the inner portion of the anulus, and the nucleus. Although studies have shown that the disc height and disc area also change nominally as disc degeneration progresses, the same disc geometry was used in both models.

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TABLE I Material Properties in the Outer Anulus for Healthy and Degenerated Discs Used in Finite Element Models^*

		Permeability (m⁴ N^-1 s^-1)
Degeneration Grade	Water Content (%)	kx	ky	kz	Porosity	Young's Modulus (MPa)	Poisson's Ratio	Aggregate Modulus (MPa)	Nonlinear Stiffness Coefficient
I (Normal)	65	1.68E-15	1.68E-15	1.64E-15	0.73	2.56	0.4	0.44	2.7
IV (Degenerated)	50	1.01E-15	1.01E-15	1.82E-15	0.57	12.29	0.35	0.93	0.44

The material properties for the outer anulus were taken from Gu WY, Mao XG, Foster RJ, Weidenbaum M, Mow VC, Rawlins BA. The anisotropic hydraulic permeability of human lumbar anulus fibrosus. Influence of age, degeneration, direction, and water content. Spine. 1999;24:2449-55

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TABLE I Material Properties in the Outer Anulus for Healthy and Degenerated Discs Used in Finite Element Models^*

		Permeability (m⁴ N^-1 s^-1)
Degeneration Grade	Water Content (%)	kx	ky	kz	Porosity	Young's Modulus (MPa)	Poisson's Ratio	Aggregate Modulus (MPa)	Nonlinear Stiffness Coefficient
I (Normal)	65	1.68E-15	1.68E-15	1.64E-15	0.73	2.56	0.4	0.44	2.7
IV (Degenerated)	50	1.01E-15	1.01E-15	1.82E-15	0.57	12.29	0.35	0.93	0.44

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TABLE II Material Properties in the Inner Anulus for Healthy and Degenerated Discs Used in Finite Element Models^*

		Permeability (m⁴ N^-1 s^-1)
Degeneration Grade	Water Content (%)	kx	ky	kz	Porosity	Young's Modulus (MPa)	Poisson's Ratio	Aggregate Modulus (MPa)	Nonlinear Stiffness Coefficient
I (Normal)	72	1.87E-15	1.87E-15	1.56E-15	0.78	2.56	0.4	0.27	2.7
IV (Degenerated)	55	1.11E-15	1.11E-15	1.76E-15	0.60	12.29	0.35	0.78	0.44

The material properties for the inner anulus were taken from Gu WY, Mao XG, Foster RJ, Weidenbaum M, Mow VC, Rawlins BA. The anisotropic hydraulic permeability of human lumbar anulus fibrosus. Influence of age, degeneration, direction, and water content. Spine. 1999;24:2449-55

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TABLE II Material Properties in the Inner Anulus for Healthy and Degenerated Discs Used in Finite Element Models^*

		Permeability (m⁴ N^-1 s^-1)
Degeneration Grade	Water Content (%)	kx	ky	kz	Porosity	Young's Modulus (MPa)	Poisson's Ratio	Aggregate Modulus (MPa)	Nonlinear Stiffness Coefficient
I (Normal)	72	1.87E-15	1.87E-15	1.56E-15	0.78	2.56	0.4	0.27	2.7
IV (Degenerated)	55	1.11E-15	1.11E-15	1.76E-15	0.60	12.29	0.35	0.78	0.44

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TABLE III Material Properties in the Nucleus for Healthy and Degenerated Discs Used in Finite Element Models^*

		Permeability (m⁴ N^-1 s^-1)
Degeneration Grade	Water Content (%)	kx	ky	kz	Porosity	Young's Modulus (MPa)	Poisson's Ratio	Aggregate Modulus (MPa)	Nonlinear Stiffness Coefficient
I (Normal)	85	2.13E-15	2.13E-15	1.45E-15	0.83	1.0	0.49	0.27	2.7
IV (Degenerated)	76	1.55E-15	1.55E-15	1.52E-15	0.71	1.66	0.40	0.45	0.44

The material properties for the nucleus were taken from Gu WY, Mao XG, Foster RJ, Weidenbaum M, Mow VC, Rawlins BA. The anisotropic hydraulic permeability of human lumbar anulus fibrosus. Influence of age, degeneration, direction, and water content. Spine. 1999;24:2449-55

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TABLE III Material Properties in the Nucleus for Healthy and Degenerated Discs Used in Finite Element Models^*

		Permeability (m⁴ N^-1 s^-1)
Degeneration Grade	Water Content (%)	kx	ky	kz	Porosity	Young's Modulus (MPa)	Poisson's Ratio	Aggregate Modulus (MPa)	Nonlinear Stiffness Coefficient
I (Normal)	85	2.13E-15	2.13E-15	1.45E-15	0.83	1.0	0.49	0.27	2.7
IV (Degenerated)	76	1.55E-15	1.55E-15	1.52E-15	0.71	1.66	0.40	0.45	0.44

To determine how cyclic loading affects the biomechanical characteristics of a degenerated lumbar disc, the results of the healthy disc finite element model and the degenerated disc finite element model were compared at the end of four hours of cyclic loading. The finite element models were loaded in axial compression at a frequency of one cycle per minute, with a uniform set of tractions acting perpendicular to the upper end-plate surface. The load varied from F_max to 40% of F_max. F_max was applied for 1.5 seconds and reduced to 40% of F_max for 1.5 seconds. The reduced load (40% of F_max) was held constant for fifty-seven seconds. The disc heights at the tenth cycle and at the 240th cycle were compared with the initial disc height to determine the loss in disc height.

Figure 1 compares the loss in disc height as a function of maximum applied load as predicted by the two finite element models representing healthy and degenerated discs. Results are presented at the maximum load during the tenth cycle as well as at the 240th cycle, to understand how disc degeneration affects the biomechanical properties both during early stages of cyclic loading as well as after a considerable number of load cycles. Both in normal and degenerated discs, the disc height loss was larger during the 240th cycle of loading than during the early stages of cyclic loading. Cyclic loading also showed that normal discs are much more deformable than degenerated discs, as evidenced by the result that the disc height loss for all loading values in degenerated discs was less than that seen in healthy discs. At a peak load of 2000 N, grade-I disc height loss increased from 2.5 mm at the tenth loading cycle to 4.5 mm at the 240th. The corresponding disc height loss was 1.0 mm to 1.8 mm in a degenerated disc. The stiffness of a healthy disc with 2000-N peak load decreased from 800 N/mm at the tenth cycle of loading to 444 N/mm at the 240th cycle of loading, indicating that stiffness decreased as the load cycle increased. At large compressive loads (3000 N), an increase in disc height loss of 48% was observed in healthy discs during the 240th cycle of loading as compared with the disc height loss during the tenth cycle of loading. The corresponding increase in disc height loss in degenerated discs was 40% during the 240th cycle. At smaller compressive loads (1000 N), healthy discs showed an increase in disc height loss of 110% at the 240th cycle of loading compared with disc height loss at the tenth cycle of loading. However, at these smaller compressive loads, there was no change in disc height loss in degenerated discs as the number of load cycles increased.

Poroelastic Finite Element Model to Predict Initiation and Progression of Disc Failure

Initiation and propagation of different types of mechanical events that lead to or promote disc degeneration and the effect of the degenerative process on the mechanical performance of the disc was studied in our laboratory using the poroelastic model of a lumbar motion segment. Failure initiation and progression (based on von Mises stress) under cyclic loading was monitored in over 50,000 points in the anulus and in about 7500 locations in the end plates using a custom-written failure rule. This rule dictated that failure at any point in a single element (twenty-seven points were considered in each element that modeled the intervertebral disc) was predicted to occur if the internal stress at that point exceeded an assumed failure stress value. If failure within an element was predicted to occur at any point in a disc component due to the applied load, the corresponding elastic material property at that location was reduced by a percentage of the intact elastic modulus for subsequent analyses; thus, it was possible to control the growth of failure progression. The physiologic loading conditions used in this investigation involved simulating the pulling of a box with a force of 140 N with use of a handle at 142 cm above the ground. Five cycles of activity per minute was modeled in the current study. During each cycle, the push-pull activity was completed in five seconds, followed by a rest for seven seconds. The rest period was simulated by applying an axial compressive load of 400 N. The percentage of disc failure volume at the end of each load cycle was calculated by dividing the number of failed points by the total number of monitored points in the disc.

Failure was found to propagate when the elastic modulus of the failed disc components was decreased in the subsequent analyses by a specified percentage of the corresponding intact elastic modulus (Fig. 2). The analyses also showed that the rate at which the disc failure volume increased with increasing load cycle (slope of the curve) was greater as the failure-induced decrease in elastic modulus was increased.

Conclusions and Discussion

Disc degeneration is a very complex phenomenon that will require extensive research both biomechanically and biochemically before it can be fully understood. The primary interest in using finite element simulations of the intervertebral disc is to understand the relationships between the biomechanical performance of the disc and disc degeneration.

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Fig. 2: Failure progression due to cyclic loading increased as the assumed elastic modulus of the failed disc component decreased due to the presence of failure.

A number of different approaches have been used to address the issue of disc degeneration, including clinical studies, experimental studies (both in vivo and in vitro studies), and computational studies. The finite element method is the most popular numerical tool currently used in spine biomechanics because of its ability to model tissues with complex properties, model the complex loading system that the spine experiences, and accurately duplicate the complex geometry of the spine. Another compelling reason to use finite element modeling is its ability to parametrically alter one input factor and analyze the effect on the results.

Only a few poroelastic finite element models that include strain-dependent swelling pressure and permeability of the disc tissues are described in the literature. With the model developed in our laboratory, we were able to predict changes in disc height during loading and unloading that were comparable with those observed in vivo because of the inclusion of swelling pressure and strain-dependent permeability and the variability of poroelastic material properties within the disc.

In the model, as the number of cycles of loading of healthy discs increased, disc height loss at peak load also increased, due to a larger amount of fluid continuously moving out of the disc; however, this may be attributed to not providing enough time for the disc to completely relax. Disc height loss at peak load during early stages of the cyclic loading as well as after 240 cycles of loading in healthy discs was greater than the corresponding loss of height in degenerated discs, indicating that the fluid flow in and out of the disc is greater in healthy discs. At large peak loads, disc height loss was also greater in the healthy disc, which may be due in part to deformation of the solid matrix. This increased deformation of the solid matrix may result in further injury to the disc. In both healthy and degenerated discs for a particular peak load, stiffness decreased as the number of load cycles increased. This is in contrast to what was observed in vivo. This discrepancy may be due to exclusion of muscle activity from the model. Electromyography used in conjunction with the in vivo testing suggested that the increased laxity of the surrounding musculature plays a significant role in the response of the spine to differing loading conditions¹⁴.

The poroelastic model was able to predict the initiation and progression of failure due to cyclic loading in a lumbar motion segment. The results showed that with a custom-written failure rule incorporated in the model, it is possible to control the progression of the failure by appropriately reducing the elastic modulus of the failed component.

To study the biomechanics of a lumbar motion segment under cyclic or repetitive loading conditions, a clear understanding of the unique interaction between the solid porous matrix and the fluid volume (or phase) becomes necessary. The finite element model can provide a method by which the fluid flow characteristics can be studied under various physiologic loading conditions. However, a complete understanding of behavior of the intervertebral disc can only be approached with use of a combination of computational models and simulations, such as the models presented here, together with in vitro and in vivo experimental methods. ?

References

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Topics

intervertebral disc ; permeability ; degenerative disc disease ; tissue degeneration

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Raghu N. Natarajan, Jamie R. Williams, Gunnar B.J. Andersson; Modeling Changes in Intervertebral Disc Mechanics with Degeneration. The Journal of Bone & Joint Surgery. 2006 Apr;88(suppl_2):36-40.

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